Again, only a tiny fraction of a civilization needs to be motivated to expand for a civilization effectively be a fully expanding civilization.
1/1,000, 1/1,000,000 ... it doesn't matter how small the fraction is to start.
Affluence in humans vastly increases consumption. By several orders of magnitude. Billionaires enjoy jets, yachts, and build companies that use vast resources to accomplish new things.
AI isn't going to be concerned about human lifetimes. 20 years to the nearest star for a laser sail ship smaller than a human takes physics we have now. For nano tech that would be a massive ship.
If you want a teleological argument, here is one: Life expands by colonizing and adapting to new environments and inventing new capabilities. Then expanding and adapting over and over again in response to each wave of change. Life expanding across the galaxy will produce beauty and complexity we can't imagine.